In this paper, we obtain the sharp uniqueness for an inverse $ x $-source problem a one-dimensional time-fractional diffusion equation with zeroth-order term by minimum possible lateral Cauchy data. The key ingredient is unique continuation which holds weak solutions.

We study the homology of dual de Rham complex as functors on category abelian groups. give a description up to degree 7 for free groups and present corrected version proof Jean’s computations zeroth group.

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain variable, which are difficult to project onto; and (b) or that admit efficient projection. Problems this form arise frequently in context semidefinite programming as well when various NP-hard solved approximately via relaxation. Since projection onto first set i...

This letter presents an almost sure convergence of the zeroth-order mirror descent (ZOMD) algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provides noisy function value at any desired point. We approximate subgradient objective using Nesterov’s Gaussian Approximation (NGA) with certain alternations suggested by some practical applications. prove iterate...